ISBN-10: 0470084065

ISBN-13: 9780470084069

Edition: 2nd 2008 (Revised)

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Casey Cobb is Associate Professor of Education Policy and Director of the Center for Education Policy Analysis at the University of Connecticut. His current research interests include policies on accountability, school choice, and bilingual education, where he examines the implications for equity among historically marginalized populations. He teaches courses in policy studies, research methods and evaluation. Casey has also served as evaluator on several projects, most recently working with the Connecticut Department of Education to study inter-district magnet programs.

Introduction

Why Statistics?

Descriptive Statistics

Inferential Statistics

The Role of Statistics in Educational Research

Variables and Their Measurement

Some Tips on Studying Statistics

Descriptive Statistics

Frequency Distributions

Why Organize Data?

Frequency Distributions for Quantitative Variables

Grouped Scores

Some Guidelines for Forming Class Intervals

Constructing a Grouped-Data Frequency Distribution

The Relative Frequency Distribution

Exact Limits

The Cumulative Percentage Frequency Distribution

Percentile Ranks

Frequency Distributions for Qualitative Variables

Summary

Graphic Representation

Why Graph Data?

Graphing Qualitative Data: The Bar Chart

Graphing Quantitative Data: The Histogram

The Frequency Polygon

Comparing Different Distributions

Relative Frequency and Proportional Area

Characteristics of Frequency Distributions

The Box Plot

Summary

Central Tendency

The Concept of Central Tendency

The Mode

The Median

The Arithmetic Mean

Central Tendency and Distribution Symmetry

Which Measure of Central Tendency to Use?

Summary

Variability

Central Tendency Is Not Enough: The Importance of Variability

The Range

Variability and Deviations from the Mean

The Variance

The Standard Deviation

The Predominance of the Variance and Standard Deviation

The Standard Deviation and the Normal Distribution

Comparing Means of Two Distributions: The Relevance of Variability

In the Denominator: n vs. n - 1

Summary

Normal Distributions and Standard Scores

A Little History: Sir Francis Galton and the Normal Curve

Properties of the Normal Curve

More on the Standard Deviation and the Normal Distribution

z Scores

The Normal Curve Table

Finding Area When the Score Is Known

Reversing the Process: Finding Scores When the Area Is Known

Comparing Scores from Different Distributions

Interpreting Effect Size

Percentile Ranks and the Normal Distribution

Other Standard Scores

Standard Scores Do Not "Normalize" a Distribution

The Normal Curve and Probability

Summary

Correlation

The Concept of Association

Bivariate Distributions and Scatterplots

The Covariance

The Pearson r

Computation of r: The Calculating Formula

Correlation and Causation

Factors Influencing Pearson r

Judging the Strength of Association: r[superscript 2]

Other Correlation Coefficients

Summary

Regression and Prediction

Correlation versus Prediction

Determining the Line of Best Fit

The Regression Equation in Terms of Raw Scores

Interpreting the Raw-Score Slope

The Regression Equation in Terms of z Scores

Some Insights Regarding Correlation and Prediction

Regression and Sums of Squares

Measuring the Margin of Prediction Error: The Standard Error of Estimate

Correlation and Causality (Revisited)

Summary

Inferential Statistics

Probability and Probability Distributions

Statistical Inference: Accounting for Chance in Sample Results

Probability: The Study of Chance

Definition of Probability

Probability Distributions

The Or/addition Rule

The And/multiplication Rule

The Normal Curve as a Probability Distribution

"So What?" Probability Distributions as the Basis for Statistical Inference

Summary

Sampling Distributions

From Coins to Means

Samples and Populations

Statistics and Parameters

Random Sampling Model

Random Sampling in Practice

Sampling Distributions of Means

Characteristics of a Sampling Distribution of Means

Using a Sampling Distribution of Means to Determine Probabilities

The Importance of Sample Size (n)

Generality of the Concept of a Sampling Distribution

Summary

Testing Statistical Hypotheses about [Mu] When [sigma] Is Known: The One-Sample z Test

Testing a Hypothesis about [Mu]: Does "Homeschooling" Make a Difference?

Dr. Meyer's Problem in a Nutshell

The Statistical Hypotheses: H[subscript 0] and H[subscript 1]

The Test Statistic z

The Probability of the Test Statistic: The p Value

The Decision Criterion: Level of Significance ([alpha])

The Level of Significance and Decision Error

The Nature and Role of H[subscript 0] and H[subscript 1]

Rejection versus Retention of H[subscript 0]

Statistical Significance versus Importance

Directional and Nondirectional Alternative Hypotheses

Prologue: The Substantive versus the Statistical

Summary

Estimation

Hypothesis Testing versus Estimation

Point Estimation versus Interval Estimation

Constructing an Interval Estimate of [Mu]

Interval Width and Level of Confidence

Interval Width and Sample Size

Interval Estimation and Hypothesis Testing

Advantages of Interval Estimation

Summary

Testing Statistical Hypotheses about [Mu] When [sigma] Is Not Known: The One-Sample t Test

Reality: [sigma] Often Is Unknown

Estimating the Standard Error of the Mean

The Test Statistic t

Degrees of Freedom

The Sampling Distribution of Student's t

An Application of Student's t

Assumption of Population Normality

Levels of Significance versus p Values

Constructing a Confidence Interval for [Mu] When [sigma] Is Not Known

Summary

Comparing the Means of Two Populations: Independent Samples

From One Mu to Two

Statistical Hypotheses

The Sampling Distribution of Differences Between Means

Estimating [Characters not reproducible]

The t Test for Two Independent Samples

Testing Hypotheses about Two Independent Means: An Example

Interval Estimation of [Mu subscript 1] - [Mu subscript 2]

Appraising the Magnitude of a Difference: Measures of Effect Size for X[subscript 1]-X[subscript 2]

How Were Groups Formed? The Role of Randomization

Statistical Inferences and Nonstatistical Generalizations

Summary

Comparing the Means of Dependent Samples

The Meaning of "Dependent"

Standard Error of the Difference Between Dependent Means

Degrees of Freedom

The t Test for Two Dependent Samples

Testing Hypotheses about Two Dependent Means: An Example

Interval Estimation of [Mu subscript D]

Summary

Comparing the Means of Three or More Independent Samples: One-Way Analysis of Variance

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